A time-domain finite-difference scheme is used to solve the elastic equation of motion. Stability, computational efficiency, and accuracy are three important problems in a numerical analysis using a time-domain finite-difference scheme. Various methods for computing elastic wavefields using time-domain finite-difference schemes have been developed, but a method of suitably realizing stability, computational efficiency, and optimal accuracy at the same time has not previously been presented.
For example, the time-domain finite-difference scheme disclosed in Non-Patent Document 1 provides a method of calculating an elastic wavefield with high efficiency and high accuracy, but is not guaranteed to be stable.
Here, “high efficiency” means that the computational resources required to obtain a specific computational accuracy are minimized. In particular, it can be said that schemes with a small calculation time and minimal bandwidths of the finite-difference operators used in the calculations have high efficiency. An “optimally accurate scheme” denotes a scheme which requires the minimum amount of computation, as compared to other schemes of the same general type, to achieve a given level of computational accuracy. Hereinafter, an “optimally accurate operator” means an operator satisfying the condition (Equation 9, to be described below), which was disclosed in Non-Patent Document 2.
[Non-Patent Document 1] Takeuchi, N., and R. J. Geller, 2000, Physics of the Earth and Planetary Interiors, 119, 99-131
[Non-Patent Document 2] R. J. Geller, and N. Takeuchi, 1995, Geophysical Journal International, 123, 449-470
[Non-Patent Document 3] R. J. Geller, and N. Takeuchi, 1998, Geophysical Journal International, 135, 48-62.